A poroelastic plate model obtained by simultaneous homogenization and dimension reduction
arxiv(2024)
摘要
In this paper, the starting point of our analysis is coupled system of
elasticity and Stokes equation. We consider two small parameters: the thickness
h of the thin plate and the pore scale ε(h) which depend on h.
We will focus specifically on the case when the pore size is small relative to
the thickness of the plate. The main goal here is derive a model for a
poroelastic plate from the 3D problem as h goes to zero using simultaneous
homogenization and dimension reduction techniques. The obtained model
generalizes the poroelastic plate model derived by A. Mikelić et. al. in 2015
by dimension reduction techniques from 3D Biot's equations in the sense that
it also covers the case of contact of poroelastic and elastic plate as well as
the evolution equation with inertia term.
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